figure-gradient-descent.tex

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\pgfplotsset{
  colormap={whitered}{color(-1cm)=(orange!75!red);color(1cm)=(white)}
}
\begin{tikzpicture}[
  declare function = {mu1=1;},
  declare function = {mu2=2;},
  declare function = {sigma1=0.5;},
  declare function = {sigma2=1;},
  declare function = {normal(\m,\s)=1/(2*\s*sqrt(pi))*exp(-(x-\m)^2/(2*\s^2));},
  declare function = {bivar(\ma,\sa,\mb,\sb)=1/(2*pi*\sa*\sb) * exp(-((x-\ma)^2/\sa^2 + (y-\mb)^2/\sb^2))/2;}]
  \footnotesize{
  {
  \begin{scope}
  \begin{axis}[
    colormap name  = whitered,
    width          = 8cm,
    height         = 5cm,
    view           = {20}{45},
    enlargelimits  = false,
    grid           = major,
    domain         = -1:3,
    y domain       = 0:4,
    samples        = 30,
    xlabel         = ${\bm \theta}^{[1]}$,
    ylabel         = ${\bm \theta}^{[2]}$,
    xlabel style   = {xshift=0em,yshift=0.8em},
    ylabel style   = {xshift=0.2em,yshift=0.8em},
    zlabel         = {$J({\bm \theta})$},
    ztick          = {-0.1},
    colorbar,
    colorbar style = {
      at     = {(1.2,0.5)},
      anchor = north west,
      ytick  = {0,-0.1},
      height = 0.25*\pgfkeysvalueof{/pgfplots/parent axis height},
      title  = {}
    }
  ]

    \addplot3 [surf] {-bivar(mu1,sigma1,mu2,sigma2)};

    \node [circle,fill=red,minimum size=3pt,inner sep=1.5pt] () at (axis cs:0.5,2,-0.01) {};

    \draw [->,very thick,ublue] (axis cs:0.5,2,-0.01) -- (axis cs:0.8,1.6,-0.03) node [pos=1,right,inner sep=2pt] {\tiny{-$\frac{\partial J({\bm \theta})}{\partial {\bm \theta}}$}};
    \draw [->,very thick,dotted] (axis cs:0.5,2,-0.01) -- (axis cs:0.2,1.5,-0.03);
    \draw [->,very thick,dotted] (axis cs:0.5,2,-0.01) -- (axis cs:0.2,3.5,-0.03);
    %\draw [black!50] (axis cs:0,-1,0) -- (axis cs:0,4,0);

  \end{axis}
  \end{scope}
  }
  }
\end{tikzpicture}

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